Recently, he's become more active in supporting team owner Dan Snyder's quest to keep the Redskins name over objections from those who contend it's a racial slur.
Moseley drew national attention - a significant amount of it negative - for his comments on NewsChannel 8's SportsTalk program a week ago that began with him proclaiming he's never, ever heard any of "these Indians" complain about the nickname.
A week later, Moseley is at it again: "I'm telling you," he said in an interview with the Associated Press, "somebody would have to drop a bomb on FedEx Field to get us to change (the name)."
Moseley said he has seen the debate over the team's name come and go since the 1970s, usually as a flash-in-the-pan topic that disappears after a day or so.
This time is different as the campaign to ditch "Redskins" has reached unprecedented momentum over the last 18 months.
Moseley now concedes that the debate shows no signs of abating, but also told the AP: "It is such a ridiculous subject."
With both sides digging in, the words are getting nastier, and there's no real possibility of compromise: Either the name stays or it goes.
Theories abound as to why Snyder, Moseley and others are on the defensive like never before over the name.
"Politicians," said Joe Theismann, Washington's Super Bowl-winning quarterback in the 1982 season and another supporter of the name. "It's an election year."
Possible Democratic presidential candidate Hillary Clinton has called it "insensitive." Fifty Democratic senators equated the name to "racism and bigotry." Maryland Gov. Martin O'Malley, who is mulling a run for president, said it is "probably time" for the name to change. President Barack Obama said he would "think about changing" the name if he owned the team.
But the politicians were late-comers. A confluence of events -- and several missteps by Snyder and his organization -- has made the issue a topic du jour.
It started with a February 2013 symposium on mascot history at the Smithsonian that left a 20-year-old Redskins fan so embarrassed that he took over his team gear and said: "I really don't feel right wearing this stuff now."
That was soon followed by the latest hearing in a long-running case brought by a group of Native Americans intent on stripping the team of its trademark protection -- the U.S. Patent and Trademark Office eventually ruled against the Redskins, but the case will likely be tied up in the courts for years. Then, last spring, the opposition got an unexpected boost from Snyder himself. The owner has always vowed never to change the name, but he came across as especially strident when he told USA Today: "We'll never change the name. It's that simple. NEVER -- you can use caps."
Soon, the Oneida Indian Nation in New York had joined the fray as a major player, buying television and radio ads in major markets -- including one that ran during the NBA finals here on ABC 7. Now, every time the team does anything to promote the name, Oneida counters with a news release within minutes. The anti-"Redskins" coalition never had an ally like it.
"They really put a lot of effort and personal time -- and the important thing, money -- into what we were doing," said Suzan Shown Harjo, a longtime lead figure in the trademark case. "We've never had money before. We've always done this on a wing and a prayer."
When Snyder started an Original Americans Foundation to give financial support to Native American tribes, Harjo called it "somewhere between a PR assault and bribery." When a major sector of the United Church of Christ was preparing a vote to boycott the Redskins, the team tried to make its case by having three self-identified members of the Blackfeet Nation call church leader Rev. John Deckenback on the phone, but Deckenback said the three didn't really push the team's cause and called the interaction a "somewhat weird experience."
A blogger hired by the Redskins to defend the team's name quit after two weeks. The team tried to make it a big deal when a self-proclaimed Native American in favor of the name arrived two weeks ago at training camp, giving him a VIP pass and making him available to the media, but the man was a D.C.-area native who couldn't spell the name of the tribe he said he was representing. When the team unveiled a "Redskins Facts" website aimed at boosting support for the name, The Washington Post examined the "facts" as presented and awarded the team a score of Three Pinocchios for leaving a "false impression."
On his Redskins-owned radio station, ESPN 980 AM, Snyder last week derided the "fun, chit-chat, cocktail talk about the name" and said detractors should be focusing more on the plight of Native Americans. His opponents point out that Snyder paid no heed to Native issues during his first 14 years as an owner and made it a focus only after the name debate swelled late last year.
"Dan Snyder's comments are proof that he is living in a bigoted billionaire bubble," was the Oneida Nation's predictably swift response. "For him to claim that a racial slur is 'fun' is grotesque."
Opponents see the rising opposition as part of a constant drip, drip, drip of anti-Redskins sentiment they hope will prevail.
"We're in this until the name changes," Oneida representative Ray Halbritter said.
But such inevitability, it would seem, is clearly not felt in the Snyder camp.